Te Kete Ipurangi Navigation:

Te Kete Ipurangi

Te Kete Ipurangi user options:

GM5-7: Construct and describe simple loci.

Elaboration on this Achievement Objective: 

This means that students will draw the graph of linear and simple quadratic equations. They will also be able to identify the linear equation for the graph of a given simple loci.

parabola and straight line.

They will also describe the common properties of points on a circle or ellipse and recognise the circle as a special case of the ellipse.




All points on a circle are the same distance from the centre. That distance is the radius.     



All points on an ellipse share a common sum of distances to two foci. As the foci close the ellipse “morphs” into a circle.


Teaching resources for this Achievement Objective:

Conic Cuts

  • Figure It Out activities
  • Geometry and Measurement
  • Level Five

This is a level 5 geometry strand activity from the Figure It Out series.

Sailing with Maths

  • Figure It Out activities
  • Number and Algebra
  • Level Five

This is a level 5 number, measurement, and geometry activity from the Figure It Out theme series.

The Running track

  • Rich learning activities
  • Geometry and Measurement
  • Level Five

The purpose of this multi-level task is to engage students in an investigation that requires them to define the dimensions of the parameters necessary to construct a described locus.

Ruler and Compass Constructions

  • Units of Work
  • Geometry and Measurement
  • Level Five

In this unit we use rulers and compasses to construct perpendicular lines and to bisect angles. These constructions are used to make a variety of polygons, nets and to illustrate loci.